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On the Construction of the Conjugate Hull of Brandt Semigroups

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Acta Mathematica Sinica,English Series 1998年第4期14卷 519-526页

作者： Zhang Moucheng, department of mathematics, South{2. Normal university, Guangzhou 510631,{2.Kan Haibing, Institute of mathematics, Fudan university, Shanghai 2.0433,{2.Li Yonghua, department of mathematics, Yunnan university, Kunming 650000,{2. department of mathematics, South{2. Normal university, Guangzhou 510631,{2. department of mathematics South China Normal University Institute of mathematics Fudan University department o] mathematics Yunnan University

In this paper the characterizations of conjugate hulls Ψ(S), φ(S), T(S) and θ(S) on a Brandt semigroup S are given. By using these results we can prove that T(S) is self-conjugate in Ψ(S) for a Brandt semigroup S.

关键词： Conjugate hull Self-conjugate Linked bitranslation Brandt semigroup

Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order

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Wuhan university Journal of Natural Sciences 2005年第2期10卷 339-343页

作者： HAN Hui-li 1,2.,DU Jin-yuan 1,3 1. School of mathematics and Statistics, Wuhan university, Wuhan 430072. Hubei,{2. 2. School of mathematics and Computer, Ningxia university, Yinchuan 75002., Ningxia,{2. 3. department of mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei,{2. Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Ningxia university School of Mathematics and Computer Yinchuan Ningxia China (GRID:grid.260987.2) (ISNI:***) Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Hubei Institute for Nationalities Department of Mathematies Enshi Hubei China (GRID:grid.34418.3a) (ISNI:***)

We have discussed and solved the boundary value problem with period 2.π and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio... 详细信息

关键词： boundary value problem singular integral equation the singularities of high order

Extremal problems on the Hua domain of the first type

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Science china mathematics 2005年第z1期48卷 343-354页

作者： SU Jianbing & YIN Weiping mathematics department, Xuzhou Normal {2., Xuzhou 2.1116, china mathematics department, Capital Normal {2., Beijing 100037, china 1. mathematics department Xuzhou Normal University 221116 Xuzhou China 2. mathematics department Capital Normal University 100037 Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.

Extremal problems on the generalized Hua domain of the first type

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Progress in Natural Science:Materials International 2006年第4期16卷 352-358页

作者： SU Jianbing and YIN Weiping department of mathematics, Xuzhou Normal {2., Xuzhou 2.1116, china department of mathematics, Capital Normal {2., Beijing 100037, china [a]department of mathematics Xuzhou Normal University Xuzhou China [b]department of mathematics Capital Normal University Beijing China

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.

关键词： extremal problem generalized Hua domain of the first type minimal circumscribed Hermitian ellipsoid.

A Note on the Multifractal Decomposition of Directed Graph Self Similar Sets

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Wuhan university Journal of Natural Sciences 2004年第3期9卷 269-272页

作者： Zheng Shui-cao 1,2., Hu Di-he 1 1. School of mathematics and Statistics, Wuhan university , Wuhan 430072. Hubei,{2. 2. The Basic Teaching department, Jimei university, Xiamen 36102., Fujian,{2. Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Jimei university The Basic Teaching Department Xiamen Fujian China (GRID:grid.411902.f) (ISNI:***) Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e., dimK u a =DimK u a =f(a), wheref is the multifractal spectral function of the directed graph self similar measure, Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping. Key words Hausdorff dimension - Hausdorff measure - multifractal decomposition CLC number O 2.1. 6 Foundation item: Supported by the National Natural Science Foundation of china (10371092. and the Foundation of Wuhan universityBiography: Zheng Shui-cao (1973-), male, Ph. D candidate, research direction: stochastic processes and random fractals.

关键词： Hausdorff dimension Hausdorff measure multifractal decomposition

The Degree of Symmetry of Certain Compact Smooth Manifolds II

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Chinese Annals of mathematics,Series B 2007年第2期28卷 195-204页

作者： Bin XU department of mathematics, {2. of Science and Technology of china, Hefei 2.002., china Chern Institute of mathematics, Nankai {2., Tianjin 300071, china department of mathematics, Johns Hopkins {2., Baltimore, MD 2.2.8, USA. department of mathematics University of Science and Technology of ChinaHefei 230026 China

We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2.V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.

关键词： Degree of symmetry Fiber bundle Cobordism Non-positive Curvature Harmonic map First cohomology

THE CODIMENSION FORMULA ON AF-COSUBMODULES

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Chinese Annals of mathematics,Series B 2002年第3期23卷 419-424页

作者： GUO KUNYU department of mathematics, Fudan {2., Shanghai 2.0433, china department of mathematics Fudan University Shanghai 200433 China

Let M1, M2.be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2.and dimM1/M2.= k < '. If M2.is an AF-cosubmodule, then the codimension dimM1/M2.of M2.in M1 equals the cardinality of zeros of M2.rel... 详细信息

Let M1, M2.be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2.and dimM1/M2.= k 2.is an AF-cosubmodule, then the codimension dimM1/M2.of M2.in M1 equals the cardinality of zeros of M2.related to MI by counting multiplicities. The codimension formula has some interesting applications. In particular, the author calculates out the dimension of Rudin quotient module, which is raised in [14].

关键词： AF-cosubmodule Characteristic space Analytic Hilbert module

Extension of isometries on the unit sphere of l^p (Γ) space

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Science china mathematics 2010年第4期53卷 1085-1096页

作者： FANG XiNian 1,& WANG JianHua 2.1 School of mathematics and Statistics,Nanjing Audit university,Nanjing 2.002.,{2. 2.department of mathematics,Anhui Normal university,Wuhu 2.1000,{2. 1. School of mathematics and Statistics Nanjing Audit University Nanjing 210029 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 < p < ∞,p≠2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto ... 详细信息

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley’s problem.

关键词： isometric extension l p (Γ) space isometry 1-Lipschitz mapping

A note on characterization of Hardy space H^1

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Science china mathematics 2005年第4期48卷 448-455页

作者： WANG Silei department of mathematics, Zhejiang {2., Hangzhou 31002., china 1. department of mathematics Zhejiang University 310028 Hangzhou China

An all-round answer is given to the following question: 'Find a necessary and sufficient size condition for an integrable compactly supported function on Rn with mean value zero to be in the Hardy space H1.' Stefanov ... 详细信息

关键词： Hardy space Riesz transform Hilbert transform